Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T13:34:31.207Z Has data issue: false hasContentIssue false

On the integration of deterministic opinions into mortality smoothing and forecasting

Published online by Cambridge University Press:  09 February 2022

Viani Biatat Djeundje*
Affiliation:
University of Edinburgh, United Kingdom

Abstract

Modelling and forecasting mortality is a topic of crucial importance to actuaries and demographers. However, forecasts from the majority of mortality projection models are continuations of past trends seen in the data. As such, these models are unable to account for external opinions or expert judgement. In this work, we present a method for the incorporation of deterministic opinions into the smoothing and forecasting of mortality rates using constraints. Not only does our approach yield a smooth transition from the past into the future, but also, the shapes of the resulting forecasts are governed by a combination of the opinion inputs and the speed of improvements observed in the data. In addition, our approach offers the possibility to compute the amount of uncertainty around the projected mortality trends conditional on the opinion inputs, and this allows us to highlight some of the pitfalls of deterministic projection methods.

Type
Original Research Paper
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andreev, K.F. & Vaupel, J.W. (2006). Forecasts of Cohort Mortality after Age 50. Max Planck Institute for Demographic Research.Google Scholar
Biatat, V. & Currie, I.D. (2010). Joint models for classification and comparison of mortality in different countries. In Proceedings of 25rd International Workshop on Statistical Modelling (pp. 8994).Google Scholar
Bjõrck, A. (1996). Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
Brouhns, N., Denuit, M. & Vermunt, J. (2002). A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31, 373393.Google Scholar
Cairns, A.J.G., Blake, D. & Dowd, K. (2006). A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. Journal of Risk and Insurance, 73, 687718.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Ong, A. & Balevich, I. (2009). A quantitative comparison of stochastic mortality models using data from England Wales and the United States. North American Actuarial Journal, 13, 135.CrossRefGoogle Scholar
Cairns, A.J.G. (2017). A Flexible and Robust Approach to Modelling Single Population Mortality. Longevity 13, Taipei, September 2017.Google Scholar
Carballoa, A., Durbán, M. & Lee, D.J. (2017). A general framework for prediction in penalized regression. Universidad Carlos III de Madrid Working Papers.Google Scholar
Continuous Mortality Investigation (2006). Working Paper 38. A Prototype Mortality Projections Model: Part One - An Outline of the Proposed Approach.Google Scholar
Continuous Mortality Investigation Bureau (2009). Working Papers 39. A Prototype Mortality Projections Model, Part Two - Detailed Analysis.Google Scholar
Continuous Mortality Investigation (2014). Working Paper 74. The CMI Mortality Projections Model, CMI2014.Google Scholar
Continuous Mortality Investigation (2016). Working Paper 91. CMI Mortality Projections Model consultation - technical paper.Google Scholar
Continuous Mortality Investigation (2020). Working Paper 129: “CMI Mortality Projections Model: CMI 2019” (2020)Google Scholar
Currie, I.D. (2015). Smoothing constrained GLMs and improving Lee-Carter Forecasts. Universidad Carlos III de Madrid, May 2015.Google Scholar
Currie, I.D., Durban, M. & Eilers, P.H.C. (2004). Smoothing and forecasting mortality rates. Statistical Modelling, 4,279298.CrossRefGoogle Scholar
Currie, I.D., Durban, M. & Eilers, P.H.C. (2006). Generalized linear array models with applications to multidimensional smoothing. Journal of the Royal Statistical Society (Series B), 68, 259280.CrossRefGoogle Scholar
Currie, I. (2013). Smoothing constrained generalized linear models with an application to the Lee-Carter model. Statistical Modelling, 13, 6993.CrossRefGoogle Scholar
Debón, A., Martnez-Ruiz, F. & Montes, F. (2010). A geostatistical approach for dynamic life tables: the effect of mortality on remaining lifetime and annuities. Insurance: Mathematics and Economics, 47, 327336.Google Scholar
Debón, A., Montes, F. & Sala, R. (2006). A comparison of nonparametric methods in the graduation of mortality: application to data from the Valencia region (Spain). International Statistical Review. Available online at the address https://doi.org/10.1111/j.1751-5823.2006.tb00171.x.CrossRefGoogle Scholar
Delwarde, A., Denuit, M. & Eilers, P.H.C. (2006). Smoothing the Lee-Carter and Poisson log-bilinear models for mortality forecasting: a penalised likelihood approach. Statistical Modelling, 7, 2948.CrossRefGoogle Scholar
Djeundje, V.A.B. & Currie, I.D. (2010). Smoothing dispersed counts with applications to mortality data. Annals of Actuarial Science, 5, 3352.CrossRefGoogle Scholar
Djeundje, V.A.B. (2011). Hierarchical and Multidimensional Smoothing with Applications to Longitudinal and Mortality Data. Heriot-Watt University, UK. Willey.Google Scholar
Eilers, P.H.C. & Marx, B.D. (1996). Flexible smoothing with B-splines and penalties. Statistical Sciences, 11, 89121.CrossRefGoogle Scholar
Eilers, P.H.C. & Marx, B.D. (2010). Splines, knots, and penalties. Computational Statistics, 2, 637653.Google Scholar
French, D. and O’Hare, C. (2014). Forecasting death rates using exogenous determinants. Journal of Forecasting, 33, 640650.CrossRefGoogle Scholar
Hoerl, A.E. & Kennard, R.W. (1970). Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12, 5567.CrossRefGoogle Scholar
Human Mortality Database. University of California, Berkeley (USA) and Max Planck Institute for Demographic Research (Germany). Available online at the address www.mortality.org.Google Scholar
Janssen, F. & Kunst, A. (2007). The choice among past trends as a basis for the prediction of future trends in old-age mortality. Popul Stud (Camb), 61, 315326.CrossRefGoogle ScholarPubMed
Janssen, F., Van Wissen, L. & Kunst, A. (2013). Including the smoking epidemic in internationally coherent mortality projections. Demography, 50, 13411362.CrossRefGoogle ScholarPubMed
Lee, D.J. & Durban, M. (2011). P-spline ANOVA-type interaction models for spatio-temporal smoothing. Statistical Modelling, 11, 4969.CrossRefGoogle Scholar
Lee, R.D. & Carter, L.R. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association, 87, 659671.Google Scholar
Ludkovski, M., Risk, J. & Zail, H. (2018). Gaussian process models for mortality rates and improvement factors. Astin Bulletin, 48, 13071347.CrossRefGoogle Scholar
McCullagh, P. & Nelder, J.A. (1989). Generalized Linear Models. Chapman and Hall.CrossRefGoogle Scholar
O’Sullivan, F. (1986). A statistical perspective on ill-posed inverse problems (with discussion). Statistical Sciences, 1, 505527.Google Scholar
Peristera, P. & Kostaki, A. (2005). An evaluation of the performance of kernel estimators for graduating mortality data. Journal of Population Research, 22, 185197.CrossRefGoogle Scholar
Plat, R. (1986). On stochastic mortality modeling. Insurance: Mathematics and Economics, 45, 393404.Google Scholar
Preston, S.H., Stokes, A., Mehta, N.K. & Cao, B. (2014). Projecting the effect of changes in smoking and obesity on future life expectancy in the United States. Demography, 51, 2749.CrossRefGoogle ScholarPubMed
Renshaw, A.E. & Haberman, S. (2006). A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38, 556570.Google Scholar
Richards, S.J. (2009). Stabilising projections. Available online at the address https://www.longevitas.co.uk/site/informationmatrix/stabilisingprojections.html4 Google Scholar
Richards, S.J., Currie, I.D., Kleinow, T. & Ritchie, G.P. (2017). A stochastic implementation of the APCI model for mortality projections. Actuarial Research Centre (ARC).Google Scholar
Richards, S.J., Currie, I.D. & Ritchie, G.P. (2014). A Value-at-Risk framework for longevity trend risk. British Actuarial Journal, 19, 116139.CrossRefGoogle Scholar
Searle, S.R., Casella, G. & McCulloch, C.E. (2006). Variance Components. Willey.Google Scholar
Stoeldraijer, L., van Duin, C., van Wissen, L. & Janssen, F. (2013). Impact of different mortality forecasting methods and explicit assumptions on projected future life expectancy: the case of the Netherlands. Demographic Research, 29, 323354.CrossRefGoogle Scholar
Strang, G. (1986). Introduction to Applied Mathematics (pp. 96107). Wellesley-Cambridge Press.Google Scholar
Willets, R.C. (1999). Mortality in the next millennium. Staple Inn Actuarial Society.Google Scholar
Willets, R. (2004). The cohort effect: insights and explanations. British Actuarial Journal, 10, 833877.CrossRefGoogle Scholar
Woods, S. (2016). Reflections on the 2015 Solvency II internal model approval process. Bank of England Prudential Regulation Authority.Google Scholar